We all live by faith in our presuppositions.
I am willing to admit and logically defend mine, are you?

Faith is believing in that for which there is no evidence. As an atheist, I have no presuppositions to defend, I merely lack a belief in any deity. You can defend yours to your heart's content.

So you don't presuppose naturalism?
How does allowing for the supernatural fit into a consistent atheistic worldview? You are probably not consistent in your beliefs, very few self professed atheists are when pressed to the logical conclusions of the worldview they claim.

You really should stop trying to tell me what I think and what my worldview is, and if it's consistent or not, you are displaying a very arrogant attitude by assuming that you know me and know what I think. Yes, all that composes atheism is a lack of belief in any deity. The supernatural, along with any and everything else, is not something that atheism concerns itself with, only a lack of belief in any deity. That is all that all atheists have in common. There are some that believe in the supernatural, others that don't, it has nothing to do with atheism. Personally, I do not, as I have never seen any evidence for it whatsoever, nor has anyone else, the only thing that anyone has ever offered for its existence is testimony, just like the belief in god, neither of which is real.

If "all that composes atheism is a lack of belief in any deity" then dogs and cats are atheists as well. You probably find yourself in good company then!

You are not the first atheist I have encountered that doesn't understand what composes what they claim to believe.
You have been exposed to the idea of a deity therefore you have had to make cognizant decision to reject that idea and embrace you "lack of belief." Even if you do presuppose naturalism like you say, and are more consistent in your worldview than many who do not, you still have an incomplete definition of what atheism is because you are denying the human component of rejecting some ideas and embracing others.
That doesn't even get into the logical impossibilities of an atheistic naturalistic worldview.

Why stop there? Also, babies, buildings, and baseball bats. Why? Because it is the default position. It wouldn't be necessary to have a lack of belief, if there weren't people who said that you should have one to begin with. Which wouldn't be bad, if it were based on evidence and reality instead of assertions with no evidence. Apparently, I find myself the company of everything and everyone un some humans think it's a good idea to believe in something for which there is no proof, and insist that the rest of us do so as well.

You are far from the first theist to be so arrogant as to tell me that I don't understand my own beliefs. I could certainly say the same of you, and then twist your beliefs to be whatever I said they were, and then make the bald-faced claim that you don't understand your own beliefs. I guess you are gonna ignore my suggestion that you speak for yourself instead of trying to speak for me and failing miserably. You can't read my mind, and you do not know my opinion unless I tell you what it is. As long as you persist in telling me what I think, then I am done having a pointless conversation with you. Good day sir.